actually anyone can run a site that contains copyrighted material if they adhere to local copyright laws - the actual jurisdiction is the main sticking point but the US DMCA laws seem dominant and US courts seem to usually assert jurisdiction, which matters if the people involved in running the site are US citizens.
As long as a web site follows the DMCA laws regarding "Safe Harbor", they are immune from prosecution for any copyrights infringing on behalf of its users. These regulations include things like honoring takedown notices, not promoting or "inciting" copyright infringement by users, and things like that.
Odysseus